In theoretical computer science, in particular in formal language theory, Kleene's algorithm transforms a given nondeterministic finite automaton (NFA) into a regular expression. Together with other conversion algorithms, it establishes the equivalence of several description formats for regular languages. Alternative presentations of the same method include the "elimination method" attributed to Brzozowski and McCluskey, the algorithm of McNaughton and Yamada, and the use of Arden's lemma. == Algorithm description == According to Gross and Yellen (2004), the algorithm can be traced back to Kleene (1956). A presentation of the algorithm in the case of deterministic finite automata (DFAs) is given in Hopcroft and Ullman (1979). The presentation of the algorithm for NFAs below follows Gross and Yellen (2004). Given a nondeterministic finite automaton M = (Q, Σ, δ, q0, F), with Q = { q0,...,qn } its set of states, the algorithm computes the sets Rkij of all strings that take M from state qi to qj without going through any state numbered higher than k. Here, "going through a state" means entering and leaving it, so both i and j may be higher than k, but no intermediate state may. Each set Rkij is represented by a regular expression; the algorithm computes them step by step for k = -1, 0, ..., n. Since there is no state numbered higher than n, the regular expression Rn0j represents the set of all strings that take M from its start state q0 to qj. If F = { q1,...,qf } is the set of accept states, the regular expression Rn01 | ... | Rn0f represents the language accepted by M. The initial regular expressions, for k = -1, are computed as follows for i≠j: R−1ij = a1 | ... | am where qj ∈ δ(qi,a1), ..., qj ∈ δ(qi,am) and as follows for i=j: R−1ii = a1 | ... | am | ε where qi ∈ δ(qi,a1), ..., qi ∈ δ(qi,am) In other words, R−1ij mentions all letters that label a transition from i to j, and we also include ε in the case where i=j. After that, in each step the expressions Rkij are computed from the previous ones by Rkij = Rk-1ik (Rk-1kk) Rk-1kj | Rk-1ij Another way to understand the operation of the algorithm is as an "elimination method", where the states from 0 to n are successively removed: when state k is removed, the regular expression Rk-1ij, which describes the words that label a path from state i>k to state j>k, is rewritten into Rkij so as to take into account the possibility of going via the "eliminated" state k. By induction on k, it can be shown that the length of each expression Rkij is at most 1/3(4k+1(6s+7) - 4) symbols, where s denotes the number of characters in Σ. Therefore, the length of the regular expression representing the language accepted by M is at most 1/3(4n+1(6s+7)f - f - 3) symbols, where f denotes the number of final states. This exponential blowup is inevitable, because there exist families of DFAs for which any equivalent regular expression must be of exponential size. In practice, the size of the regular expression obtained by running the algorithm can be very different depending on the order in which the states are considered by the procedure, i.e., the order in which they are numbered from 0 to n. == Example == The automaton shown in the picture can be described as M = (Q, Σ, δ, q0, F) with the set of states Q = { q0, q1, q2 }, the input alphabet Σ = { a, b }, the transition function δ with δ(q0,a)=q0, δ(q0,b)=q1, δ(q1,a)=q2, δ(q1,b)=q1, δ(q2,a)=q1, and δ(q2,b)=q1, the start state q0, and set of accept states F = { q1 }. Kleene's algorithm computes the initial regular expressions as After that, the Rkij are computed from the Rk-1ij step by step for k = 0, 1, 2. Kleene algebra equalities are used to simplify the regular expressions as much as possible. Step 0 Step 1 Step 2 Since q0 is the start state and q1 is the only accept state, the regular expression R201 denotes the set of all strings accepted by the automaton.
The 2028 Global Intelligence Crisis
The 2028 Global Intelligence Crisis is a report authored by James van Geelen and Alap Shah and published by Citrini Research in February 2026, on the impact of artificial intelligence on humanity's future. Written in the form of a scenario analysis, it was viewed millions of times online and reportedly caused a fall in the stock market prices of major tech and financial firms. It also received criticism among others, for its allegedly flawed economic logic. The 'thought exercise', as the authors called it, painted a gloomy picture for the near future, where outputs keep growing while consumer's ability to spend collapses. "...driven by ai agents that don’t sleep, take sick days or require health insurance”, "outputs that are shown in national accounts increases, "but never circulates through the real economy"(which the report calls 'Ghost GDP'), the authors argued. In other words, the authors predict a scenario where the owners of the AI firms will accumulate a vast fortune but there will be scant demand from consumers as AI would cause massive unemployment. The authors caution the reader that what they make is a scenario and not a prediction. In the scenario they visualise, any service whose value proposition is “I will navigate complexity that you find tedious” is getting disrupted. The reports argues that the unique ability of human beings to analyse, decide, create, persuade, and coordinate was “the thing that could not be replicated at scale,” and call the historical scarcity of this precious entity 'friction'. When this friction becomes zero, a gamut of changes occur which then triggers a cascading of changes across the economy. ”Travel booking platforms are an early casualty; Financial advice. tax prep., and routine legal work follow suit. National unemployment rate go as high 10.2% and the S&P 500 goes for a massive 38% peak-to-trough crash. In contrast to the previous technological revolutions the high-earning professionals suffers more and get forced to take up roles in the gig economy. Labour supply becomes abundant and this cuts wages all across the economy. The dent in income for the employees then affects other sectors of the economy such as the residential mortgage market. The losses for the software companies triggers loan defaults and heralds peril for the private credit sector.
Adaptive neuro fuzzy inference system
An adaptive neuro-fuzzy inference system or adaptive network-based fuzzy inference system (ANFIS) is a kind of artificial neural network that is based on Takagi–Sugeno fuzzy inference system, a class of fuzzy models introduced by Tomohiro Takagi and Michio Sugeno for system identification and control. The technique was developed in the early 1990s. Since it integrates both neural networks and fuzzy logic principles, it has potential to capture the benefits of both in a single framework. Its inference system corresponds to a set of fuzzy IF–THEN rules that have learning capability to approximate nonlinear functions. Hence, ANFIS is considered to be a universal estimator. For using the ANFIS in a more efficient and optimal way, one can use the best parameters obtained by genetic algorithm. It has uses in intelligent situational aware energy management system. == ANFIS architecture == It is possible to identify two parts in the network structure, namely premise and consequence parts. In more details, the architecture is composed by five layers. The first layer takes the input values and determines the membership functions belonging to them. It is commonly called fuzzification layer. The membership degrees of each function are computed by using the premise parameter set, namely {a,b,c}. The second layer is responsible of generating the firing strengths for the rules. Due to its task, the second layer is denoted as "rule layer". The role of the third layer is to normalize the computed firing strengths, by dividing each value for the total firing strength. The fourth layer takes as input the normalized values and the consequence parameter set {p,q,r}. The values returned by this layer are the defuzzificated ones and those values are passed to the last layer to return the final output. === Fuzzification layer === The first layer of an ANFIS network describes the difference to a vanilla neural network. Neural networks in general are operating with a data pre-processing step, in which the features are converted into normalized values between 0 and 1. An ANFIS neural network doesn't need a sigmoid function, but it's doing the preprocessing step by converting numeric values into fuzzy values. Here is an example: Suppose, the network gets as input the distance between two points in the 2d space. The distance is measured in pixels and it can have values from 0 up to 500 pixels. Converting the numerical values into fuzzy numbers is done with the membership function which consists of semantic descriptions like near, middle and far. Each possible linguistic value is given by an individual neuron. The neuron “near” fires with a value from 0 until 1, if the distance is located within the category "near". While the neuron “middle” fires, if the distance in that category. The input value “distance in pixels” is split into three different neurons for near, middle and far.
Cube 3D
Cube 3D is an artificial intelligence model that is developed by Roblox Corporation. It is open source and available on GitHub and Hugging Face. In March 2026, Roblox announced Cube 3D as a mesh generation model that takes text input. In February 2026, Roblox released 4D creation in a public beta, allowing embedding Cube 3D into Roblox games. Cube 3D is integrated into Roblox Studio and its API, and supports two modes of 4D creation. == History == In March 2025, Roblox announced Cube 3D as a mesh generation model that takes text input. Its first feature was an API that allows mesh generation. That month, it was made open source. Over 1.8 million assets have been generated by Cube 3D since March 2025. In March 2025, 4D creation was announced. That November, 4D creation was released in early access. In February 2026, Roblox released 4D creation in a public beta, allowing embedding Cube 3D into Roblox games. == Technology == Cube 3D is trained on Roblox meshes. To generate meshes, it tokenises meshes and shapes and predicts the next token. Cube 3D is integrated into Roblox Studio and the Roblox Studio API. Its API allows mesh generation. In 4D creation, two modes can be used. Car-5 supports modular objects, and Body-1 only supports single-mesh objects.
Data processing unit
A data processing unit (DPU) is a programmable computer processor that tightly integrates a general-purpose CPU with network interface hardware. They are also occasionally called "IPUs" (infrastructure processing unit) or "SmartNICs". They can be used in place of traditional NICs to relieve the main CPU of complex networking responsibilities and other "infrastructural" duties; although their features vary, they may be used to perform encryption/decryption, serve as a firewall, handle TCP/IP, process HTTP requests, or even function as a hypervisor or storage controller. These devices can be attractive to cloud computing providers whose servers might otherwise spend a significant amount of CPU time on these tasks, cutting into the cycles they can provide to guests. They see use in other kinds of data center environments as well due to their improved power consumption efficiency for routine networking tasks compared to general-purpose CPUs.
Podium (company)
Podium is a private technology company headquartered in Lehi, Utah that develops cloud-based software related to messaging, customer feedback, online reviews, selling products, and requesting payments. == History == Podium was founded in 2014 by Eric Rea and Dennis Steele, who developed a tool to help small businesses "build their online reputation" through online reviews. Podium was initially known as RepDrive before rebranding as Podium in 2015. In 2015, Podium moved from a spare bedroom to a new location above a Provo bike shop. In March 2020, Podium added payments technology to its product suite. In November 2021, Podium raised $201 million in Series D funding and was valued at $3 billion. == Product == Podium is a software-as-a-service platform designed to improve business online reputation. It helps users manage business interactions in one tool. Users can communicate reviews, texts, chats, and post payment directly within the app.
Yu-Gi-Oh! VRAINS
Yu-Gi-Oh! VRAINS (遊☆戯☆王VRAINS, Yū Gi Ō Vureinzu) is a Japanese anime series created and animated by Nihon Ad Systems (NAS) and Gallop. It is the fifth anime spin-off in the Yu-Gi-Oh! franchise. The series aired in Japan on TV Tokyo from May 10, 2017 to September 25, 2019. It was simulcast outside of Asia by Crunchyroll courtesy of Konami Cross Media NY. It premiered in the United States on November 3, 2020 on Pluto TV. The term 'VRAINS' derives from 'Virtual Reality' (VR), 'Artificial Intelligence' (AI), 'Network System' (NS). The series revolves around the exploits of the protagonist Yusaku within the virtual world named VRAINS. In addition to featuring previous summoning mechanics, VRAINS introduces the new "Link Summon" mechanic. The series was succeeded by Yu-Gi-Oh! Sevens, which premiered in Japan on April 4, 2020. == Plot == In a place known as Den City, thousands of duelists take part in a virtual reality space known as LINK VRAINS, created by SOL Technologies, where users can create unique avatars and participate in games of Duel Monsters with each other. As a mysterious hacker organization known as the Knights of Hanoi, led by Varis, threatens this world, a high-school student and hacking genius named Yusaku Fujiki battles against them under the guise of Playmaker. Both the Knights and SOL Technologies are also after a peculiar self-aware artificial intelligence program, who holds the key to a secret area inside the network named the Cyberse World, which the Knights of Hanoi seek to destroy. As the series begins, Yusaku sees the chance to capture this AI, which he names Ai, who sets off a digital maelstrom in LINK VRAINS known as the Data Storm. As the appearance of this storm gives birth to Speed Duels, in which duellists surf the wind as they duel, Yusaku battles against Hanoi in order to uncover the truth concerning an incident that happened to him 10 years ago. With the help of two Charisma Duellists, Go Onizuka (Japanese) and Skye Zaizen, who uses the alias Blue Angel (season 1), and Blue Maiden (season 2 onwards) online, Playmaker is able to defeat Varis, saving the entire network and part ways with Ai who decides to return to his own world, the Cyberse World. Three months after Hanoi's fall, Ai discovers the Cyberse World destroyed and his friends nowhere to be found, prompting him to return to Yusaku. Meanwhile, Yusaku once again fights as Playmaker after the consciousness of the younger brother of his friend, Cal Kolter, is stolen by a mysterious enemy named Bohman. In pursuit of Bohman, Yusaku and Ai are joined by Theodore Hamilton, a victim of the Lost Incident like Yusaku who uses the alias of Soulburner online and Ai's Fire Ignis friend based on Theodore, Flame. Aqua, the Water Ignis, follows soon after by becoming Skye's partner. At the same time, Varis revives Knights of Hanoi to fight against the new enemies. It's revealed that Bohman is a sentient AI created by the Light Ignis, Lightning, who reveals that he's the one who destroyed the Cyberse World and steals Cal's brother's consciousness. Deeming Ignis superior, he decides to destroy humanity. The Wind Ignis, Windy, also assists Lightning after his program was forcefully rewritten. To defeat Lightning's team, Yusaku and his friends join forces with Knights of Hanoi and enter Lightning's stronghold. Both sides fight until only Playmaker, Ai, and Bohman are left with the latter having absorbed all other Ignis. Before perishing, both Flame and Aqua give Ai the last of their powers, allowing him and Playmaker to defeat Bohman. After the fight against Bohman, LINK VRAINS is shut down and Ai disappear together with Yusaku's robot, Roboppi. Replacing LINK VRAINS, SOL Technology develops a humanoid robot SOLtis, which Ai and Roboppi uses to infiltrate SOL Technology and attack its high executive, Queen. Knowing he'll be the next target, Skye's older brother, Akira, enlists the help of Playmaker and his friends as well as Knights of Hanoi once more to protect him. Ai and Roboppi manage to defeat everyone except Playmaker, Soulburner, and Varis, who are forced to fight decoys. After defeating Akira and taking over SOL Technology, Ai reopens LINK VRAINS and delivers a message for Playmaker that tells the whereabout of his location. Yusaku confronts Ai alone, leading the two of them to duel. Ai explains that Lightning left behind a simulation that shows the world will be destroyed if Ai is the only Ignis left. Fearing that he'll become like Lightning and Bohman, Ai decides to end his life either by Playmaker's hand if he loses or by scattering his free will into the SOLtis if he wins. Despite Playmaker's attempt to dissuade Ai, he still refuses to back down, forcing Playmaker to defeat him. In his last moment, Ai reveals that within the simulations, Yusaku always ends up dying protecting him, which is a future that he wishes to avoid. Three months after the final battle, everyone moves on with their lives and Yusaku goes on a journey. Somewhere within the network, Ai is revealed to be alive. == Production == Yu-Gi-Oh! VRAINS was first announced on December 16, 2016. It began airing on TV Tokyo in Japan on May 10, 2017. The series is being directed by Masahiro Hosoda at Studio Gallop with screenplay by Shin Yoshida and character design by Ken'ichi Hara. It would be the final anime series in the franchise to be animated by Gallop; Bridge would animate future instalments beginning with Yu-Gi-Oh! Sevens. The series ended on September 25, 2019. The series is being simulcast with English subtitles outside of Asia by Crunchyroll. This makes it the first series in the Yu-Gi-Oh! franchise to receive an official simulcast alongside its Japanese broadcast. A localized English adaptation was produced by Konami Cross Media NY. The pilot episode was previewed along with a digitally remastered screening of Yu-Gi-Oh! The Movie: Pyramid of Light on March 11, 2018 and March 12, 2018 in the US, and on June 13, 2018 in the UK. The English dub began airing on Teletoon in Canada on September 1, 2018, and on 9Go! in Australia on April 6, 2019. In November 2020, Cinedigm announced that the streaming service Pluto TV has secured exclusive rights in multiple territories, including the United States and Latin America, to VRAINS. Pluto TV would launch a channel dedicated to the Yu-Gi-Oh! franchise, featuring episodes from the entire Yu-Gi-Oh! Duel Monsters metaseries, including VRAINS, available in English and dubbed in multiple languages. == Trading Card Game == Yu-Gi-Oh! VRAINS introduces new gameplay elements to the Yu-Gi-Oh! Trading Card Game. With the release of the "Link Strike Starter Deck", it introduced the New Master Rules (also known as Master Rule 4 in some countries) to the competitive field of play. Now, only one monster can be summoned directly from each player's Extra Deck at a time, which is placed in one of the two new zones in the middle of the field called the "Extra Monster Zone". Complementing this new gameplay element are the new Link Monsters, honey-comb blue colored monsters that go into your Extra Deck. They do not have "Levels" or "Ranks", but instead have a "Link Rating", which indicates the number of arrows on the card and the required number of monsters required to summon them. A Link Monster's Link Rating can also be used as a number of materials for a Link Summon depending on their rating, subtracted from the Link Monster the player wishes to summon. Link Monsters have a number of Link Arrows equal to their Link Rating that point either vertically, horizontally, and/or diagonally. These Link Arrows that point to an empty Main Monster Zone allow the player to summon monsters from the Extra Deck, which include face-up Pendulum Monsters. The two Pendulum Zones have been moved to the far ends of the Spell & Trap Zones, though they also double as regular Spell & Trap Zones should the player wish not to use them. In 2019, a new format exclusive to the TCG was introduced separate from the main game, known as Speed Duels. The rules are similar to the main game and parallel the formatting used in the mobile game Duel Links. A format meant as a beginner's introduction to the basics, both the field and each player's decks have been drastically simplified to reflect that. Decks contain only 20-30 cards, each player gets only three Main Monster zones, and a turn will immediately end following the Battle Phase. Exclusive to Speed Duels, each player is allowed one Skill Card, which a player places face down during the beginning of a duel and can use anytime. == Reception == The series ranked 52 in Tokyo Anime Award Festival in Best 100 TV Anime 2017 category. The series' rank rose up to 8 in the same award in 2020 with 28,369 votes.